Bio-sensing using toroidal microresonators & theoretical cavity optomechanics

In this thesis we report on two matters, (i) time-resolved single
particle bio-sensing using a cavity enhanced refractive index
sensor with unmatched sensitivity, and (ii) the theoretical
analysis of parametric normal mode splitting in cavity
optomechanics, as well as the quantum limit of a displacement
transducer that relies on multiple cavity modes. It is the unifying
element of these studies that they rely on a high-Q optical cavity
transducer and amount to a precision measurement of an optical
frequency. In the first part, we describe an experiment where a
high-Q toroidal microcavity is used as a refractive index sensor
for single particle studies. The resonator supports whispering
gallery modes (WGM) that feature an evanescent fraction, probing
the environment close to the toroid's surface. When a particle with
a refractive index, different from its environment, enters the
evanescent field of the WGM, the resonance frequency shifts. Here,
we monitor the shift with a frequency resolution of df/f=7.7e-11 at
a time resolution of 100µs , which constitutes a x10 improvement of
the sensitivity and a x100 improvement in time resolution, compared
to the state of the art. This unprecedented sensitivity is the key
to real-time resolution of single lipid vesicles with 25nm radius
adsorbing onto the surface. Moreover -- for the first time within
one distinct measurement -- a record number of up to 200
identifiable events was recorded, which provides the foundation for
a meaningful statistical analysis. Strikingly, the large number of
recorded events and the high precision revealed a disagreement with
the theoretical model for the single particle frequency shift. A
correction factor that fully accounts for the polarizability of the
particle, and thus corrects the deviation, was introduced and
establishes a quantitative understanding of the binding events.
Directed towards biological application, we introduce an elegant
method to cover the resonator surface with a single lipid bilayer,
which creates a universal, biomimetic interface for specific
functionalization with lipid bound receptors or membrane proteins.
Quantitative binding of streptavidin to biotinylated lipids is
demonstrated. Moving beyond the detection limit, we provide
evidence that the presence of single IgG proteins (that cannot be
resolved individually) manifests in the frequency noise spectrum.
The theoretical analysis of the thermo-refractive noise floor
yields a fundamental limit of the sensors resolution. The second
part of the thesis deals with the theoretical analysis of the
coupling between an optical cavity mode and a mechanical mode of
much lower frequency. Despite the vastly different resonance
frequencies, a regime of strong coupling between the mechanics and
the light field can be achieved, which manifests as a hybridization
of the modes and as a mode splitting in the spectrum of the
quadrature fluctuations. The regime is a precondition for coherent
energy exchange between the mechanical oscillator and the light
field. Experimental observation of optomechanical mode splitting
was reported shortly after publication of our results [cf.
Gröblacher et al., Nature 460, 724--727]. Dynamical backaction
cooling of the mechanical mode can be achieved, when the optical
mode is driven red-detuned from resonance. We use a perturbation
and a covariance approach to calculate both, the power dependence
of the mechanical occupation number and the influence of excess
noise in the optical drive that is used for cooling. The result was
one to one applied for data analysis in a seminal article on ground
state cooling of a mechanical oscillator [cf. Teufel et al., Nature
475, 359--363]. In addition we investigate a setting, where
multiple optical cavity modes are coupled to a single mechanical
degree of freedom. Resonant build-up of the motional sidebands
amplifies the mechanical displacement signal, such that the
standard quantum limit for linear position detection can be reached
at significantly lower input power.